Question

A metal (FW 243.7 g/mol) crystallizes into a body-centered cubic unit cell and has a radius of 1.86 Å. What is the density of this metal in g/cm3?

Answer 1

Here r = 1.86 A

r = 1.86*10^-8 cm

length of body diagonal = sqrt(a^2+a^2+a^2)

length of body diagonal = a*sqrt(3)

we have below equation to be used:

For BCC Lattice

length of body diagonal = 4*r

a*sqrt(3) = 4*r

Given: r = 1.86*10^-8 cm

So,

a = 4*r/(sqrt(3))

a = 4*1.86*10^-8/(sqrt(3)) cm

a = 4.295*10^-8 cm

Molar mass = 243.7 g/mol

since the cubic cell is Body Centred Cubic, the value of Z=2

d = (Z*M)/(a^3*NA)

d = (2*243.7)/((4.295*10^-8)^3*(6.022*10^23))

d = 10.2 g/cm^3

Answer: 10.2 g/cm^3